During the next two weeks traveling in Europe with his wife and college-student daughter, Sen. Sam Nunn may settle not only his own future but the question of whether the hammerlock held by liberal activists on the Democratic Party may actually be broken.

When he returns at the end of August, Nunn is to say whether he will run for president. A "no" will signal that nobody so conservative as this centrist Georgian can make even a serious attempt to lead the Democrats. A "yes" will set off an epochal struggle for the soul of his party.

The struggle would be much different from the eight campaigns for the presidential nomination now under way. For starters, Nunn would ignore Iowa's leadoff caucuses, where the ideological demands of liberal activists tilt all candidates leftward. Next, he would consciously fail liberal litmus tests. In private, he makes clear rank-and-file Democrats should get a choice, not an echo.

Could such an exotic path lead to the ideologized party's nominating Nunn in Atlanta? Conceivably it could -- for two peculiar reasons. First, the absence of strong front-runners could mean Iowa and New Hampshire may not significantly narrow the large Democratic field by "Super Tuesday" March 8. Second, the 11 southern primaries that day could yield a rich Nunn delegate harvest, particularly with the Rev. Jesse Jackson depriving the liberal pack of black voters. If this happened, new front-runner Nunn could then roll to nomination.

Many in the party think it cannot happen. But more important, Nunn now thinks it can. The cool, self-confident Armed Services Committee chairman needs no presidential run as a self-boosting personal ego trip. His heightened interest derives from careful reassessment of his chances.

That is reflected by a strong Nunn backer, former Democratic national chairman Robert S. Strauss. He told a political associate recently that whereas he used to consider the odds 80-20 against Nunn's running, he now considered it 50-50. "If I know Bob," the associate told us, "that means he has information that Sam will run."

Not so. The 50-50 odds are Nunn's own estimate. He did not know what he was going to do when he left for Europe a week ago with wife Colleen and daughter Michelle, a University of Virginia student. After attending Aspen Institute meetings in Lucerne, Switzerland, the Nunns will vacation at undisclosed locations, where the presidential race will be analyzed from every angle.

The reason for holding back, in fact, is family. Nunn has told friends he worries about the effect on his family, including son Brian, a high-school student. Colleen Nunn recently told a friend the odds were 80-20 against a run for the presidency. An intensely private person, she is leery of national attention.

The argument in favor of running has been made to Nunn by such supporters as Strauss, former Democratic national chairman John White and former Virginia governor Chuck Robb. Not only does Nunn appear to them to be the one Democrat who could smash Republican presidential dominance in the South, but he also appears as the one who can break the Democrats' thralldom to liberal special-interest groups.

Actually, Nunn has important closet support within those groups. Construction Workers leader Robert Georgine recently told a Nunn supporter that he "likes" the senator and that AFL-CIO president Lane Kirkland "really likes" him. But, added Georgine mournfully, Nunn's lifetime 38 percent AFL-CIO COPE voting rating makes public support from Big Labor come hard.

Nunn is no more a "movement conservative" or Reaganite in Democratic clothing than he is a liberal Democrat. Nevertheless, his 29 percent rating by the Americans for Democratic Action is about 30 points below where Rep. Richard Gephardt's was before Gephardt began retooling himself as a liberal for the presidential nomination. Nunn's ADA ratings are also 20 to 30 points below his American Conservative Union score.

Yet, Nunn will not retool if he runs. Colleagues say he was disappointed that his friend Sen. John Glenn tacked leftward in his failed 1984 campaign. Nunn probably will vote for Judge Robert Bork's confirmation, as he did for Chief Justice William Rehnquist's. He supports contra aid, and has voted to overturn the Supreme Court decision legalizing abortion.

Failing three such litmus tests disqualifies him for Iowa's caucuses. But that delights his advisers. They urge him to make one trip to Iowa, inform activists there of his views and then leave. With strategy for New Hampshire still undecided, Nunn would turn to the broader constituency of Super Tuesday. Such prospective emancipation explains why a goodly number of Democrats hope Sam Nunn comes home from Europe to say yes.